what a fun bag! I'm excited to get to cables...could you do a "flat" strap with a matching cable pattern?
Or, I saw on Knitty Gritty a twisted cord that Vicki Howell did with an electric mixer...she used 3 strands, but you could use 6 strands, 2 grouped together to get 3. Then she tied each strand to the beater of the electric mixer and the other end of the strands to something stationery. THEN she turned on the mixer and it twisted her cord just right. Before she untied it from either end, she found the center point and folded it, it twisted up and she just sort of pulled it and it was great.
That's a long explanation, but I hope it's clear. It will look braided without doing the icord or the braiding!